An Entropy-Based Goodness of Fit Statistic
for the von Mises Distribution

by Ulric J. Lund, S.R. Jammalamadaka
.

Abstract:
The maximum entropy characterization of the von Mises
distribution on the circle is exploited to derive a consistent
goodness of fit test statistic for the von Mises distribution.
Monte Carlo simulation results are tabulated giving critical
values of the test statistic for various sample sizes and values
of the concentration parameter. A power analysis is presented
for various alternative hypotheses, comparing the entropy statistic
to two competing goodness of fit statistics. The entropy statistic
is shown to compare favorably and may be more attractive, especially
considering its ease of computation. Finally, it is cautioned that
the maximum entropy statistic, which is derived under the assumption
that the mean direction is well-defined, is not appropriate for
differentiating between the von Mises and the uniform distribution
on the circle.